### abstract

- We study the subtree isomorphism problem: Given trees H and G, find a subtree of G which is isomorphic to H or decide that there is no such subtree. We give an O(~k/sup 1.8//log k\ n) time algorithm for this problem, where k and n are the number of vertices in H and G respectively. This improves over the O(k/sup 1.5/n) algorithms of Chung (1987) and Matula (1978). We also give a randomized (Las Vegas) O(min(k/sup 1.45/n, kn/sup 1.43/))-time algorithm for the decision problem.